Page 74 - Modeling of Chemical Kinetics and Reactor Design

44 Modeling of Chemical Kinetics and Reactor Design

Example 1-3
The Thermal decomposition of ethane to ethylene, methane, butane,
and hydrogen can be expressed by the following mechanism.

CH → 2 CH * 3 (1-190)
k 1
6
2
CH + C H  → CH + C H * 5 (1-191)

*
k 2
3
4
2
6
2

CH → CH 4 + H * (1-192)
*
k 3
2
2
5
H + C H  → H + C H * (1-193)

*
k 4
2 6 2 2 5
k
2CH → C H 10 (1-194)

*
5
2
4
5
Derive a rate law for the formation of ethylene C H assuming
2
4
k << k . The free radicals are CH , and C H .
*
*
3 5 3 2 5
Solution
*
*
Applying the steady state equations for the free radicals H , CH ,
3
*
and C H , the rate of formation of ethylene C H for a constant
2
4
2
5
volume batch reactor is:
dC
2
+ ( r ) = CH 4 = kC (1-195)
CH 4 dt 3 CH 5 *
2
2
The rate of formation of the free radicals are:
( +r ) = dC CH 3 * = kC − k C C = 0 (1-196)
2
2
CH 3 * dt 1 CH 6 2 CH 3 * CH 6
( +r ) = dC CH 5 *
2
2
CH 5 * dt
(1-197)
= kC * C + k C * C − k C 2 * = 0
2
5
4
2
2
CH 3 CH 6 H CH 6 CH 5
2